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A transmission line has 0.2 pu impedance on a base of 132 kV, 100 MVA ┬╖ On a base of 220 kV, 50 MVA, it will have a pu impedance of
0.27
0.144
0.036
11
0.036
Given: Initial impedance Z_{pu1} = 0.2, Voltage V1тАЛ = 132 kV, MVA1тАЛ = 100 MVA ┬╖ New base Voltage V2тАЛ = 220 kV, MVA2тАЛ = 50 MVA.
Initial impedance Z_{pu1} = 0.2, Voltage V1тАЛ = 132 kV, MVA1тАЛ = 100 MVA ┬╖ New base Voltage V2тАЛ = 220 kV, MVA2тАЛ = 50 MVA.
Zpu2тАЛ=Zpu1тАЛ├Ч(MVA1тАЛMVA2тАЛтАЛ)├Ч(V2тАЛV1тАЛтАЛ)2
Identify given parameters
Given parameters are Zpu1тАЛ=0.2, V1тАЛ=132┬аkV, S1тАЛ=100┬аMVA, V2тАЛ=220┬аkV, and S2тАЛ=50┬аMVA.
Zpu1тАЛ=0.2,V1тАЛ=132┬аkV,S1тАЛ=100┬аMVA,V2тАЛ=220┬аkV,S2тАЛ=50┬аMVA
Apply change of base formula
Use the formula for converting per-unit impedance from one base to another: Zpu2тАЛ=Zpu1тАЛ├Ч(S2тАЛ/S1тАЛ)├Ч(V1тАЛ/V2тАЛ)2.
Zpu2тАЛ=Zpu1тАЛ├Ч(S1тАЛS2тАЛтАЛ)├Ч(V2тАЛV1тАЛтАЛ)2
Substitute values and calculate
Substitute the values: Zpu2тАЛ=0.2├Ч(50/100)├Ч(132/220)2=0.2├Ч0.5├Ч(0.6)2.
Zpu2тАЛ=0.2├Ч0.5├Ч0.36=0.036
C is correct because the per-unit impedance on the new base is calculated as 0.036.
This change of base calculation is fundamental for solving power system fault analysis and load flow studies where components are often provided with different nominal bases.